Mixed Oligopoly under Demand Uncertainty

Abstract

In this paper we introduce product demand uncertainty in a
mixed oligopoly model and reexamine the nature of sub-game perfect
Nash equilibrium (SPNE) when firms decide in the first stage whether
to lead or follow in the subsequent quantity-setting game. In the
non-stochastic setting, Pal (1998) demonstrated that when the public
firm competes with a domestic private firm, multiple equilibria
exist but the efficient equilibrium outcome is for the public firm
to follow. Matsumura (2003a) proved that when the public firm's
rival is a foreign private firm, leadership of the public firm is
both efficient as well as SPN equilibrium. Our stochastic model
shows that when the leader must commit to output before the
resolution of uncertainty, multiple SPNE is possible. Whether the
equilibrium outcome is public or private leadership hinges upon the
degree of privatization and market volatility. More importantly,
Pareto-inefficient simultaneous production is a likely SPNE. Our
results are driven by the fact that the resolution of uncertainty
enhances the profits of the follower firm in a manner that is well
known in real option theory.